PS: This _very_ old theorem has an impeccable European lineage. Euclid proved (Book IX, Proposition 36) that ... In symbols: N(p) = 2^(p-1)*M(p) is perfect if ...
If 2^p -1 is a prime, then the sum of powers (consisting of p elements) existing between 2^p-1 and 2^2(p-1), extremes included, is a perfect. Example: p=3;...
Hi Everybody I don’t have the programs that can manipulate huge integers so I’m stuck and burning with curiosity. Can anyone calculate the next term in the...
Hello! There are some questions about GF(n,b). 1) Why GFNSieve doesn't remove b's which are odd powers of even numbers (e.g., 216)? Why doesn't Proth...
Hello, For some number theory research, I need a programming language supporting unlimited precision integers. It should run on Windows and the execution of...
Hello! It's known that the number of primes b^N+1 for fixed N=2^n and b<B is about C(n)*li(B)/N, where C(n) is constant. Some values of C(n) are given at ...
Euclid's formula concerning perfect numbers, progressively developed for all values of n -except 1- produces numbers whose last ciphers are cyclic: 6-6-8-0. ...
Hello, John McNamara has started a group called oneandthreearefourgroup to discuss Fibonacci and Lucas sequences. This is an important area for new number...
Happy New Year to all, It's starting well for me: my computers did a good job during my break holidays and found the new 388847-digit prime 857678^65536+1. Did...
Hi, I've found a bug in APSieve v0.67 - this does not effect the sieving, just the PRP testing code. The PRP testing code appears not to work at all - don't...
Dear prime hunters, number theorists and other members of our groups! Wishing you happy New Year, successful work, a lot of health, joy and friendship! ... ...
One year ago i had a found that 2^p-1 is prime when (x^(2^p-2)/p)=2^z mod 2^p-1. For all x, spezial x<>2^k Example.p=17 2^17-1 is prime, because 19^7710=2^12 ...
If the respective values of Mersenne p of perfect numbers are known, then the respective last ciphers can be calculated by the following operation: p/4. Such...
Primes Group, Regarding the inquiry about prime calendar days, New Year's Day, 1 January 2002 CE, is day number 730853, a prime number. Steve Wagler...
As you will probably know, 1729 is the smallest number expressible as the sum of two cubes in two distinct ways. (a taxicab number) Similarly, Pythagoras...
Well worth a look: http://www.users.globalnet.co.uk/~perry/maths/antidivisorother2.htm Of special interest are n=anti-tau(n)+tau(n). These numbers so far are: ...
Probably. I'll make the updates soonish - thanks for the info. Quick teaser: Prove there are an infinite number of primes that contain a particular digit. Jon...
My conjecture for the number of Carmichael numbers less than x is C(x) = ln ln ln x This comes directly from the equations on page 123 of the Crandall and...
Hello all, I was wondering if the number (2^8388608+1)/(5*2^25+1) can be tested with openpfgw.The character of this number(composite or prime) is not known,i ...
If a right triangle is constructed with one leg equal to a Mersenne prime and the other leg equal to the following power of 2, then the area of the triangle is...
Can anyone comment or find a(possible) flaw in : http://www.dybot.com/numbers/sqfree.htm __________________________________________________ Do You Yahoo!? Send...
In a posting of 2 Sep 2000 to the Mersenne list (see http://www.mail-archive.com/mersenne@.../msg05162.html) I introduced the "Gaussian Mersennes":- s[n]...
Jud McCranie found ... Maybe A(7529384362) = 973 is MAD enough to get into frame, but I'm only guessing! Seems to me there ought to be a smart way of searching...
Congrats to Bouk de Water and Marcel Martin, for disposing of yet another incomplete top-20, with the 20th proven titanic Mersenne cofactor: (2^9901-1)/( ...
